Let K be the least normal modal logic and BK its Belnapian version, which enriches K with 'strong negation'. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK.
Original language | English |
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Pages (from-to) | 3-33 |
Number of pages | 31 |
Journal | Logic and Logical Philosophy |
Volume | 25 |
Issue number | 1 |
DOIs | |
State | Published - 2016 |
Externally published | Yes |
ID: 34776042